st: coefficient explanation

Dear all,
The model I am working with now is:
y=beta1*x1+beta2*x2+u (here, beta1 is significant)
However, I realize the correlation between y and x1 is due to some other factor which is not present in the model. Therefore, I add this critical variable that can best proxy for this factor, x3, in the model. Now the model is y=beta1*x1+beta2*x2+beta3*x3+u. In this case, beta1 should weaken when x3 is present. But my question is: beta1 should have smaller magnitude than before but still significant or beta1 should be insignificant when x3 is added? If beta1 is still significant but with smaller value when x3 is added, can I say x3 is a critical value which is ignored before or correlation between y and x1 is weakened?
Any suggestion is appreciated.
Best,
Kayla
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